The evaluation of the strength distribution of silicon carbide and alumina fibres by a multi-modal Weibull distribution

Abstract

The strengh distributions of silicon carbide and alumina fibres have been evaluated by a multimodal Weibull distribution function. This treatment is based on the concept that the fracture of the fibre is determined by competition among the strength distributions of several kinds of the defect sub-population. Since those fibres were observed to have two types of fracture mode, the evaluation of a bi-modal Weibull distribution was performed in comparison with the single Weibull distribution usually employed. The accuracy of the fit for these two distributions was judged from maximum logarithm likelihoods and cumulative distribution curves. The result showed that the logarithm likelihood calculated using the bi-modal Weibull distribution function gave a larger value, as compared with those using the single Weibull distribution function. The curve predicted from the former function was also in good agreement with the data points. In addition, the strength distribution and the average value at a different gauge length were extrapolated from the Weibull parameters estimated at the original gauge length. In this case, also, the bi-modal Weibull distribution gave a more accurate prediction of the data points.